where p(t, z), ~(2, t) are the mean density and velocity of the flow, p(z, t) is the pressure. Assume the gas under consideration is polytropic. Then the temperature, density, and pressure are related with RT = p/p where R is a positive constant proportional to the molecular weight of gas and assumed to be unit for simplicity. So p = Tp. Roughly speaking, the pressure p vanishes as T goes to ze...

In a previous paper (Transp. Porous Media, 55(1): 47–70), algorithms are given for computing the analytical solution to the three-phase Riemann problem. Application of those algorithms requires that the wave configuration is known. The purpose of this note is to provide a procedure to determine the wave structure for any initial and injected saturation states.

a fundamental topic in computational fluid dynamics is the role of coordinate particularly for searching optimized coordinates. the objective of this study is the numerical modeling of supersonic flows using a new coordinate system i.e. unified coordinate system (ucs) uses moving mesh with motionless viewing window technique. ucs has an advantage over traditional coordinate systems (eulerian an...

We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics [6] for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution ...

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

This paper deals with a model for traffic flow based on a system of conservation laws [2]. We construct a solution of the Riemann Problem at an arbitrary junction of a road network. Our construction provides a solution of the full system. In particular, all moments are conserved. AMS subject classifications: 35Lxx, 35L6

Shock wave theory was studied in literature by many authors. This article presents a survey with references about various topics related to shock waves: Hyperbolic conservation laws, Well-posedness theory, Compactness theory, Shock and reaction-di¤usion wave, The CJ and ZND theory, Existence of detonation in Majda’s model, Premixed laminar ‡ame, Multidimensional gas ‡ows, Multidimensional Riema...

We study a Riemann problem for the unsteady transonic small disturbance equations that results in a diverging rarefaction problem. The self-similar reduction leads to a boundary value problem with equations that change type (hyperbolic-elliptic) and a sonic line that is a free boundary. We summarize the principal ideas and present the main features of the problem. The flow in the hyperbolic par...